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talljasperman's avatar

Do engineers really round pi to one digit (details inside)?

Asked by talljasperman (16749 points ) April 1st, 2013

Somewhere in the Flutherverse I remember a jelly saying that in his masters engineering class that they only use one significant digit for assignments… Do the full time students use 3 instead of 3.142817, or even 3.14 when building a bridge after they graduate? Can this be one of the reasons that space probes keep malfunctioning and bridges collapse? Or do different engineers have different values for pi beyond 3? ”:”

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11 Answers

gasman's avatar

Since it’s still April fool’s day, I assume this is not a serious question.

The Biblical value of pi is exactly 3, however [I Kings 7:23], so maybe Christian fundamentalist engineers use this value ;)

Hawaii_Jake's avatar

I’ll just leave this here.

Tropical_Willie's avatar

Most computer programs for geometry, use pi in it’s non-rounded form for calculations.

LuckyGuy's avatar

Back when I used my slide rule, Pi was clearly marked on the slides. The number of significant digits was purely a function of my manual dexterity.

Engineers use many significant digits. Physicists are the ones who round it to 3 or 10^0.5 or sqrt(10).

Mariah's avatar

My understanding is that some problems require more precision than others. If your calculation just calls for a “ballpark,” 3 is fine.

gasman's avatar

@LuckyGuy I grew up in the era of slide rules. Inexpensive ones were good for three significant figures (3.14). Professional grade slide rules with log-log scales were precise to four sig figs if you used them carefully. I’m sure many engineering feats were accomplished using pi = 3.142.

The square root of 10 =~ 3.1623 overestimates pi by about 0.6% – not a bad estimate, though as a college physics major I never saw anyone use it. A much better estimate is the fraction 22 / 7.

Pocket calculators hit the market just as I was leaving physics!

LuckyGuy's avatar

@gasman I thought physicists only cared about orders of magnitudes. Pi is half an order of magnitude (within .02 orders of magnitude.) ;-)
I used to put talcum powder on my slide rule to make it move smoother easier. What a tool. (Feel free to interpret that any way you like. )

gasman's avatar

@LuckyGuy Yeah, sometimes it’s hard just to guess even the correct order of magnitude. (How many particles in the observed universe? 10^80 give or take.) @Mariah is right about ballpark figures; pi=3 is more than enough accuracy for many back-of-the-envelope calculations. The log of the ratio pi:3 =~ .002—quite a small error in that sense. Like the joke about a physicist trying to predict the outcome of a horse race, succeeding only in solving for the case of a perfect sphere…

Increased precision using additional decimal places is required, however, during intermediate calculations in order to produce a final answer with the required number of decimal places. (The same is true with computers, using ‘guard bytes’ in numerical calculations.) If you’re going to round an answer to just one digit, for instance, then better to use pi = 3.1 rather than pi=3.

gasman's avatar

@LuckyGuy Please no “slipstick” jokes. I still have my slide rule & the leather loop that came with it so it can, um, hang from your pants.

LuckyGuy's avatar

@gasman I’ve still got mine, too – in the same configuration as yours. It’s a fashion statement.

Dr_Lawrence's avatar

For rough estimates, a few decimal points will do. When the outcome has profound effects on health or safety, then the use of a computer that can provide the value of Pi to 64 decimal points prevents errors of estimation especially if the calculation process employs Pi in multiple instances. Typically the final answer is rounded down to whatever number of decimal places is meaningful and relevant for the problem at hand.

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